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A 21-km horizontal very-low frequency (VLF) antenna has been constructed at Siple Station, Antarctica. This antenna is to be used to inject VLF waves into the magnetosphere in order to perform wave particle interaction experiments. In the present paper, the properties of this antenna are analyzed and its impedance and efficiency calculated. The electrical properties of the ice layer beneath the antenna are modeled. The ice is represented by several layers, each with a different dielectric constant and conductivity. A variational method due to Galejs  for an antenna in a stratified dielectric is used. In this method the cylindrical antenna is replaced by an equivalent strip antenna so that the entire geometry is planar. The efficiency is calculated as a function of frequency for different lengths of the antenna. It is found that the antenna is most efficient near its antiresonant frequency. The optimum length for efficient operation at a given frequency is discussed. It is shown that the antenna has an efficiency greater than 2 percent over more than a 2 to 1 frequency range. Some advantages of the Siple antenna, as compared with other horizontal and vertical antennas, are pointed out.